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Fundamental Phenomena in Nanoscale Semiconductor Devices
Published in Ashish Raman, Deep Shekhar, Naveen Kumar, Sub-Micron Semiconductor Devices, 2022
Zeinab Ramezani, Arash Ahmadivand
Quantum confined structures can be divided into 2D, 1D, and 0D potential wells, according to the dimensions number, in which the confined particle can move freely [81]. Two-dimensional structures are thin films in the order of a few nanometers thickness that are usually deposited on a bulk material (quantum well/superlattices). A quantum well is a special type of heterostructure in which a thin film is surrounded by two-barrier layers. Electrons and holes both experience lower energies in the well layer, which is called the potential well. Electrons and holes are the waves confined within this extremely thin layer, which is typically around 100 Å in thickness. In such structures, the allowed states correspond to standing waves to the perpendicular direction of the layers. The system is quantized due to the standing waves, which are merely particular waves, known as quantum wells [82]. Quantum wells are semiconductor structures with a thin layer, in which many quantum mechanical effects can be controlled. Most of their characteristic features are derived from the quantum confinement of electron and hole carriers in thin layers of a semiconductor material and sandwiched between the other barrier layers of the semiconductor. A particle in a box is a proper model to figure out the basic properties of a quantum well.
Materials for Nanosensors
Published in Vinod Kumar Khanna, Nanosensors, 2021
What are the implications of Equation 2.43? Equation 2.43 implies that, on decreasing the dimension L of the box, the spacing between the energy levels of the particle in the box increases (Figure 2.9). Thus, it can be said that, on constraining the charge-carrier particles within reduced dimensions, the quantum confinement effect causes a change in the density of the electronic states. For a particle that is confined in a three-dimensional box constrained by walls of infinitely high potential energy, the allowed energy states for the particle are discrete with a nonzero ground state energy. As the length of the box, which corresponds to the radius of the QD, is changed, the energy gap between the ground and the first excited state varies in proportion to 1/r2. Effect of dimensions of the box on energy-level diagrams of the particle-in-a-box: (a) large crystal and (b) small crystal. Note the change in inter-level energy differences as well as in bandgap with decrease in size of the semiconductor crystal.
Introduction to Laser
Published in Pradip Narayan Ghosh, Laser Physics and Spectroscopy, 2018
For double heterostructure lasers we need a minimum width of the active region. If the width is reduced much further to 10 nm region quantum wells are formed (Fig. 1. 14). There are discrete energy levels like particle-in-a-box system. The movements of the electrons or holes perpendicular to the layers is constrained. They move parallel to the layers virtually in two dimensions. The electron-hole recombination probability depends on the number of energy levels available close to the transition energy. In a quantum well laser this number density of states is large as the energy levels are well defined. Hence the gain intensity can be large and this can compensate the loss due to the extremely small size of the active layer. One method to increase the optical confinement is to add more quantum wells in order to produce multiple quantum well (Fig. 1.15) so that each has a confinement of the same optical mode thereby increasing the net gain. The Multiple Quantum Well (MQW) needs more threshold current since each individual well needs injected electrons. This results in higher gain and faster time response. These laser frequencies can be chosen very easily by selecting the value of d and the material. They need smaller threshold current (Eq. 1.8.6) because of having small d. So there is flexibility to increase or multiply the number of layers. They have many advantages over the DH laser diodes.
Non-uniform space filling (NUSF) designs
Published in Journal of Quality Technology, 2021
Lu Lu, Christine M. Anderson-Cook, Towfiq Ahmed
Since their introduction by McKay, Beckman, and Conover (1979), space-filling designs have proven highly effective for the exploration of input spaces and to characterize the outputs from computer models or simulators. As noted by Pronzato and Muller (2012), the statistics literature suggests that these designs often have superior properties for estimation and prediction of emulators. However, the fundamental assumption that uniformity throughout the region is universally desirable has remained largely unchallenged. Bowman and Woods (2013) proposed weighted space-filling (WSF) designs, which provide the user a flexible approach to incorporate known multivariate dependences between input variables into design selection for simulators. The method uses a user-specified weight function to reflect the input dependencies and/or prior information on the input space. Joseph et al. (2015) proposed a minimum energy design (MED) to generate design points that asymptotically follow proposed probability density function of interest. By considering each design point as a charged particle inside a box and minimizing the total potential energy of these particles, a sequential approach based on adaptively learning of the unknown response surface was proposed for generating the MED.
Exploring a spectral filtering approach to electronic structure calculations
Published in Molecular Physics, 2021
Alexis J. Kiessling, Jeffrey A. Cina
For the sake of replication of these results, we note that, for the system here, accuracy of time evolution is determined by comparison to a calculation using a discrete position basis. For metrics such as position and eigenstate fidelity, good agreement is achieved, but a large difference is found between the -widths of the wave packets. This inconsistency is a result of the initial wave packet's amplitude in unbound eigenstates. These states, which resemble particle-in-a-box states when found using a discrete position basis, have significant amplitude for values of q far from the potential's minimum. However, the ansatz is a product of a polynomial and a Gaussian; the Gaussian removes components far from its centre, which is consistently near the potential minimum. Therefore, the ansatz cannot accurately capture amplitude in these unbound states. When comparing q, this is not a problem, but the -width, which contains , gives extra weight to those far-from-the-minimum amplitudes that the ansatz cannot capture. As such, the two calculations are a poor match for this particular quantity. Note that this artifact of our fit to the intial wave packet does not compromise the fidelity of the main contributing eigenstates or their eigenenergies.